Question: Simplify the following expression: $ x = \dfrac{-2}{a - 6} + \dfrac{9}{7} $
Answer: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7}{7}$ $ \dfrac{-2}{a - 6} \times \dfrac{7}{7} = \dfrac{-14}{7a - 42} $ Multiply the second expression by $\dfrac{a - 6}{a - 6}$ $ \dfrac{9}{7} \times \dfrac{a - 6}{a - 6} = \dfrac{9a - 54}{7a - 42} $ Therefore $ x = \dfrac{-14}{7a - 42} + \dfrac{9a - 54}{7a - 42} $ Now the expressions have the same denominator we can simply add the numerators: $x = \dfrac{-14 + 9a - 54}{7a - 42} $ $x = \dfrac{9a - 68}{7a - 42}$